Skin abscesses typically go away on their own.
But since this is in the Dental Category I'm assuming you're talking about a tooth abscess?
If it's a tooth abscess then no the tooth abscess will not go away on it's own without dental treatment.
You need to get some antibiotics to treat the infection that is causing the tooth abscess.
A visit to the dentist is needed to treat a tooth abscess so it doesn't get worse.